(a) The personal representative may allow a claim, or the court or judge may approve a claim, in part. The allowance or approval shall state the amount for which the claim is allowed or approved.
(b) A creditor who refuses to accept the amount allowed or approved in satisfaction of the claim may bring an action on the claim in the manner provided in Chapter 8 (commencing with Section 9350). The creditor may not recover costs in the action unless the creditor recovers an amount greater than that allowed or approved.